In reply to L Fraser:
Not in the west of Cornwall, but if you are driving down/back you will pass it, about 15 min from the A30: Hawk's Tor on Bodmin Moor. It is less than a mile's walk from the end of the road, has short easy climbs and a walk off. I used to go there with our kids when they were young.
Further west, we also had a great morning of scrambling along the base of the Porthguarnon crag at low tide, then up and out, with six kids aged 9-15. There's a Diff there too 'Kelly's Eye' that I think I led then brought them all up.
Bosigran is great. Just scrambling in, along and out would be exciting for your children. The first actual routes you get to are top rope-able. I did Alison's Rib (D) with the kids.
Further east, there's also Roche Rock where there is (from memory of long ago) an easy slab from which I could not persuade my daughter to let go and trust the rope.
You could also have a lot of fun with your children at Gwithian beach, at the eastern end near the lighthouse. It is a bouldering venue with exciting (for children) canyons and short problems they could try, plus rock pools and sand if the climbing palls.
Post edited at 13:23